Arrange racks in upper and lower thirds of oven; preheat to 375°F. Spread out pumpkin seeds in a single layer on a rimmed baking sheet and toast on top rack, stirring once or twice, until lightly browned, puffed, and aromatic, about 7 minutes. Toss pumpkin seeds on sheet with 1 teaspoon oil and a pinch of salt. Let cool on sheet; transfer to a work surface and coarsely chop. DO AHEAD: Pumpkin seeds can be prepared 1 day ahead. Store airtight at room temperature.

Increase oven temperature to 425°F. Place squash, cut side down, on a cutting board. Using a sharp knife, carefully remove peel. Cut squash lengthwise into 3/4"-thick wedges. Place squash, 1/4 cup oil, and thyme in a large bowl. Season with salt and pepper. Toss to coat. Divide squash between 2 large rimmed baking sheets, cut side down, in a single layer.

Mix remaining 1/2 cup oil, 1/4 cup lemon juice, and parsley in a medium bowl. Season dressing with salt, pepper, and additional lemon juice, if desired. Place dandelion greens in a large bowl; drizzle with 1 tablespoon dressing. Season with salt and pepper; toss to coat. Add dates and Parmesan, if using, to remaining dressing in bowl for date relish.

Arrange dandelion greens on a large platter; top with warm squash. Spoon date relish over; garnish with pumpkin seeds.